Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ π -¹ ² ³ °

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,818

Hi;

I got - ∞ for the one with the z in there. Thanks much for providing your solution.

**In mathematics, you don't understand things. You just get used to them.**

**I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.**

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**gAr****Member**- Registered: 2011-01-09
- Posts: 3,479

Hi,

Okay.

You could've figured it out that there could be a mistake.

Thanks for telling!

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense" - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,673

hi gAr

could you explain how you got the second line in your solution.i don't get it.

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

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**gAr****Member**- Registered: 2011-01-09
- Posts: 3,479

Hi anonimnystefy,

I used L'Hospital's rule.

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense" - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,673

aah.ok think i get it.

could you also make a topic on integrals?it would be nice to practice working on them.

*Last edited by anonimnystefy (2011-06-30 01:05:20)*

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,818

**In mathematics, you don't understand things. You just get used to them.**

**I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.**

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**gAr****Member**- Registered: 2011-01-09
- Posts: 3,479

Hi bobbym,

I was searching for that url. Thanks!

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense" - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,818

Hi gAr;

I can not come up with anything better for #9 then using L'Hospitals rule.

**In mathematics, you don't understand things. You just get used to them.**

**I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.**

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**gAr****Member**- Registered: 2011-01-09
- Posts: 3,479

Okay, no problem.

Thanks for looking into the problem.

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,818

Hi;

This works. Taylorize the numerator:

Now divide through by x and now it is easy to see what the limit is.

**In mathematics, you don't understand things. You just get used to them.**

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**gAr****Member**- Registered: 2011-01-09
- Posts: 3,479

Hi bobbym,

Yes, I tried expanding like that.

But deriving that would require us to find limits anyway!

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,818

Hi;

Do you mean the derivatives, because the limits are done term by term?

Yes, you would have to find and prove the general term of that series ( done by induction ). Once you have the general term it is easy to see all terms after the constant term have an x in them and therefore zero out.

Oh wait, I see what you are saying! Good point. Even the f(0) could be a problem.

**In mathematics, you don't understand things. You just get used to them.**

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**gAr****Member**- Registered: 2011-01-09
- Posts: 3,479

Hi,

Yes!

That's why I avoided giving that in my solution.

I thought maybe we can use binomial theorem, but that too fails. (or is it me?)

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,818

Hi gAr;

That is one way, maybe.

Also this is like a piece of experimental math. You use a package to get the answer and then you prove the answer is correct by induction. Sort of like the more classical use of guessing at the solution of a sum or a recurrence.

**In mathematics, you don't understand things. You just get used to them.**

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**gAr****Member**- Registered: 2011-01-09
- Posts: 3,479

Hi bobbym,

Yes, I agree.

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,818

Hi;

In this case since proving the answer you get is going to be difficult at least from what I see, I think it is easier to use your way.

**In mathematics, you don't understand things. You just get used to them.**

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**gAr****Member**- Registered: 2011-01-09
- Posts: 3,479

Hi bobbym,

I think so. From what I know, no other tricks I can think of.

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,673

hi gAr

how about a hint on the 10?

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

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**gAr****Member**- Registered: 2011-01-09
- Posts: 3,479

Hi anonimnystefy,

It's already solved in #94.

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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**123ronnie321****Member**- Registered: 2010-09-28
- Posts: 128

I hope my steps are correct.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,673

hi 123ronnie123

how did you get the next to last line?

Here lies the reader who will never open this book. He is forever dead.

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**123ronnie321****Member**- Registered: 2010-09-28
- Posts: 128

Hi anonimnystefy,

I am unsure about the ending of my solution and I am waiting for either gAr's or Bobbym's help.

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**gAr****Member**- Registered: 2011-01-09
- Posts: 3,479

Hi 123ronnie321,

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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**123ronnie321****Member**- Registered: 2010-09-28
- Posts: 128

Thanks for your help, gAr.

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**gAr****Member**- Registered: 2011-01-09
- Posts: 3,479

Hi,

You're welcome!

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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